房地產影響因素分析

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房地產影響因素分析

房地產影響因素分析
（背景）2002年以來，我國商品房銷售額大幅攀升?帶動了房地產開發和城市基礎設施投資的新一輪高速增長。通過產業鏈的傳遞，進而又拉動鋼材、有色金屬、建材、石化等生產資料價格的快速上漲，刺激這些生產資料部門產能投資的成倍擴張，最后導致全社會固定資產投資規模過大、增速過快情況的出現。房價過快上漲在推動投資增長過快的同時，已經成為抑制消費的重要因素。
房地產價格本身呈自然上漲趨勢，房價中長期趨勢總是看漲。隨著我國經濟發展，居民可支配收入提高，民間資金雄厚，大量資金需要尋找投資渠道，而股票市場等投資渠道目前又處于低迷狀態，這是房地產投資需求不斷擴大的經濟背景。強勁的CPI上漲說明當前的房價上漲并非孤立，是有其宏觀經濟背景的。宏觀調控能否有效防止局部行業過熱出現反彈，其中的關鍵就是要繼續加強和完善對房地產業的調控。（引言）國際上關于房地產有一種普遍的觀點：人均收入超過1000美元，房地產市場呈現高速發展階段。歐美等發達國家基本都經歷了這樣一個階段。我們這篇論文，主要探討房地產影響因素分析，主要從人均收入對房地產長期發展的影響闡述。

年份 X1 X2 X3 Y
1990 2551.736 1510.16 222 704.3319
1991 1111.236 1700.6 233.3 786.1935
1992 590.5998 2026.6 253.4 994.6555
1993 2897.019 2577.4 294.2 1291.456
1994 3532.471 3496.2 367.8 1408.639
1995 3983.081 4282.95 429.6 1590.863
1996 4071.181 4838.9 467.4 1806.399
1997 3527.536 5160.3 481.9 1997.161
1998 2966.057 5425.1 479 2062.569
1999 2818.805 5854 472.8 2052.6
2000 2674.264 6279.98 476.6 2111.617
2001 2830.688 6859.6 479.9 2169.719
2002 2906.16 7702.8 475.1 2250.177
2003 3011.424 8472.2 479.4 2359.499
2004 3441.62 9421.6 495.2 2713.878

房地產影響因素分析

X1=建材成本（元/平方米） X2=居民人均收入（元）     X3=物價指數     Y=房地產價格（元/平方米）
初定模型：Y=c+a1*x1 +a2*x2 +a3*x3+et
Dependent Variable: Y
Method: Least Squares
Date: 06/05/05   Time: 23:04
Sample: 1990 2004
Included observations: 15
Variable Coefficient Std. Error t-Statistic Prob.
X3 2.537578 0.590422 4.297908 0.0013
X2 0.146495 0.020968 6.986568 0.0000
X1 -0.018016 0.035019 -0.514447 0.6171
C 33.20929 118.2747 0.280781 0.7841
R-squared 0.983094     Mean dependent var 1753.317
Adjusted R-squared 0.978483     S.D. dependent var 600.9536
S.E. of regression 88.15143     Akaike info criterion 12.01917
Sum squared resid 85477.42     Schwarz criterion 12.20798
Log likelihood -86.14376     F-statistic 213.2186
Durbin-Watson stat 1.504263     Prob(F-statistic) 0.000000

一：多元線性回歸


Dependent Variable: Y
Method: Least Squares
Date: 06/05/05   Time: 23:05
Sample: 1990 2004
Included observations: 15
Variable Coefficient Std. Error t-Statistic Prob.
X1 0.336010 0.151084 2.223999 0.0445
C 792.0169 453.4460 1.746662 0.1043
R-squared 0.275612     Mean dependent var 1753.317
Adjusted R-squared 0.219889     S.D. dependent var 600.9536
S.E. of regression 530.7855     Akaike info criterion 15.51016
Sum squared resid 3662533.     Schwarz criterion 15.60457
Log likelihood -114.3262     F-statistic 4.946171
Durbin-Watson stat 0.275870     Prob(F-statistic) 0.044490

Dependent Variable: Y
Method: Least Squares
Date: 06/05/05   Time: 23:09
Sample: 1990 2004
Included observations: 15
Variable Coefficient Std. Error t-Statistic Prob.
X3 5.501779 0.525075 10.47809 0.0000
C -486.8605 220.1227 -2.211769 0.0455
R-squared 0.894128     Mean dependent var 1753.317
Adjusted R-squared 0.885984     S.D. dependent var 600.9536
S.E. of regression 202.9191     Akaike info criterion 13.58706
Sum squared resid 535290.2     Schwarz criterion 13.68146
Log likelihood -99.90293     F-statistic 109.7903
Durbin-Watson stat 0.440527     Prob(F-statistic) 0.000000

Dependent Variable: Y
Method: Least Squares
Date: 06/05/05   Time: 23:10
Sample: 1990 2004
Included observations: 15
Variable Coefficient Std. Error t-Statistic Prob.
X2 0.236347 0.015879 14.88417 0.0000
C 561.9975 88.56333 6.345713 0.0000
R-squared 0.944572     Mean dependent var 1753.317
Adjusted R-squared 0.940308     S.D. dependent var 600.9536
S.E. of regression 146.8243     Akaike info criterion 12.93992
Sum squared resid 280245.9     Schwarz criterion 13.03432
Log likelihood -95.04937     F-statistic 221.5384
Durbin-Watson stat 0.475648     Prob(F-statistic) 0.000000

Dependent Variable: Y
Method: Least Squares
Date: 06/07/05   Time: 21:42
Sample: 1990 2004
Included observations: 15
Variable Coefficient Std. Error t-Statistic Prob.
X3 2.355833 0.458340 5.139923 0.0002
X2 0.150086 0.019157 7.834714 0.0000
C 37.56794 114.2991 0.328681 0.7481
R-squared 0.982687     Mean dependent var 1753.317
Adjusted R-squared 0.979802     S.D. dependent var 600.9536
S.E. of regression 85.40783     Akaike info criterion 11.90961
Sum squared resid 87533.98     Schwarz criterion 12.05122
Log likelihood -86.32207     F-statistic 340.5649
Durbin-Watson stat 1.408298     Prob(F-statistic) 0.000000

　　　得到結果發現，ｘ１的系數小，然后對ｙ與ｘ１回歸可決系數小，相關性差，剔出這個因素。因為價格更多取決于供需關系。
修正之后為：Y＝c+a2*x2+a3*x3＋et
二：多重線性分析：三個表如上：
X2 與X3 存在多重共線性，
1.000000 0.876073
0.876073 1.000000

Sample: 1990 2004
Included observations: 15
Variable Coefficient Std. Error t-Statistic Prob.
X2 0.236347 0.015879 14.88417 0.0000
C 561.9975 88.56333 6.345713 0.0000
R-squared 0.944572     Mean dependent var 1753.317
Adjusted R-squared 0.940308     S.D. dependent var 600.9536
S.E. of regression 146.8243     Akaike info criterion 12.93992
Sum squared resid 280245.9     Schwarz criterion 13.03432
Log likelihood -95.04937     F-statistic 221.5384
Durbin-Watson stat 0.475648     Prob(F-statistic) 0.000000

　由于引入物價指數改善小，所以模型僅一步改進為：Y＝c+a2*x2＋et

三：異方差檢驗：

ARCH Test:
F-statistic 1.315031     Probability 0.335173
Obs*R-squared 3.963227     Probability 0.265462

Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 06/05/05   Time: 23:46
Sample(adjusted): 1993 2004
Included observations: 12 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
C 22737.94 10296.61 2.208295 0.0582
RESID^2(-1) 0.241952 0.383144 0.631493 0.5453
RESID^2(-2) -0.327769 0.404787 -0.809734 0.4415
RESID^2(-3) -0.273720 0.378355 -0.723449 0.4900
R-squared 0.330269     Mean dependent var 16705.23
Adjusted R-squared 0.079120     S.D. dependent var 18205.33
S.E. of regression 17470.29     Akaike info criterion 22.63559
Sum squared resid 2.44E+09     Schwarz criterion 22.79723
Log likelihood -131.8136     F-statistic 1.315031
Durbin-Watson stat 1.842435     Prob(F-statistic) 0.335173

ＡＲＣＨ＝３．９６３＜臨界值７．８１４７３
所以無異方差

White Heteroskedasticity Test:
F-statistic 0.159291     Probability 0.854522
Obs*R-squared 0.387928     Probability 0.823687

Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 06/05/05   Time: 23:46
Sample: 1990 2004
Included observations: 15
Variable Coefficient Std. Error t-Statistic Prob.
C 31063.28 22612.20 1.373740 0.1946
X2 -5.055754 9.640127 -0.524449 0.6095
X2^2 0.000421 0.000907 0.464605 0.6505
R-squared 0.025862     Mean dependent var 18683.06
Adjusted R-squared -0.136494     S.D. dependent var 18673.13
S.E. of regression 19906.77     Akaike info criterion 22.81236
Sum squared resid 4.76E+09     Schwarz criterion 22.95397
Log likelihood -168.0927     F-statistic 0.159291
Durbin-Watson stat 1.357657     Prob(F-statistic) 0.854522

ＷＨＩＴＥ＝０．３８７９＜臨界值７．８１４７３
無異方差。

四：自相關分析：
　　ＤＷ＝０．４７５６
查表的ｄｌ＝１．０７７　　ｄｕ＝１．３６１
存在自相關
廣義差分法修正：ρ＝１－０．４７５６／２＝０．７６２２

Dependent Variable: DY
Method: Least Squares
Date: 06/06/05   Time: 00:18
Sample(adjusted): 1991 2004
Included observations: 14 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
DX2 0.182086 0.034918 5.214655 0.0002
C 236.5589 63.27388 3.738650 0.0028
R-squared 0.693820     Mean dependent var 544.1620
Adjusted R-squared 0.668305     S.D. dependent var 148.7133
S.E. of regression 85.64840     Akaike info criterion 11.86994
Sum squared resid 88027.77     Schwarz criterion 11.96124
Log likelihood -81.08959     F-statistic 27.19263
Durbin-Watson stat 1.584278     Prob(F-statistic) 0.000217

得出：回歸后可決系數降低，考慮其他方法。
1．迭代法：表：
　　發現可決系數提高，Ｆ統計量提高，ＤＷ＝１．５５４７〉１．３６１
已經無自相關。
結論：Y－bY（－１）＝ｃ*（１－ｂ）＋a2*（x2－b*x2（－１））+et

由下表的b=0.681
C=561.9975 a2=0.236347 179.2772
Y*= Y－0.681Y（－１） X*= x2－0.681*x2（－１）
Y*=179.2272 +0.2363X*+et

Method: Least Squares
Date: 06/07/05   Time: 20:57
Sample(adjusted): 1991 2004
Included observations: 14 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
E2 0.680509 0.177696 3.829624 0.0024
C 11.68773 24.88825 0.469608 0.6471
R-squared 0.549989     Mean dependent var 15.32764
Adjusted R-squared 0.512488     S.D. dependent var 133.2751
S.E. of regression 93.05539     Akaike info criterion 12.03583
Sum squared resid 103911.7     Schwarz criterion 12.12712
Log likelihood -82.25081     F-statistic 14.66602
Durbin-Watson stat 1.313042     Prob(F-statistic) 0.002397

2．改進模型方程（對數法，然后用迭代法）：Lｙ－ｂLｙ（－１）＝　ｃ＊（１－ｂ）＋ａ２＊（Lｘ２－ｂ＊Lｘ２（－１）
可決系數很高，F統計量相對1中也有提高，DW=1.81>1.361
無自相關。

Dependent Variable: LY
Method: Least Squares
Date: 06/06/05   Time: 10:24
Sample(adjusted): 1991 2004
Included observations: 14 after adjusting endpoints
Convergence achieved after 7 iterations
Variable Coefficient Std. Error t-Statistic Prob.
LX2 0.586203 0.100243 5.847799 0.0001
C 2.525810 0.882350 2.862594 0.0154
AR(1) 0.567144 0.220457 2.572589 0.0259
R-squared 0.980054     Mean dependent var 7.460096
Adjusted R-squared 0.976428     S.D. dependent var 0.351331
S.E. of regression 0.053941     Akaike info criterion -2.814442
Sum squared resid 0.032006     Schwarz criterion -2.677501
Log likelihood 22.70109     F-statistic 270.2458
Durbin-Watson stat 1.810100     Prob(F-statistic) 0.000000
Inverted AR Roots        .57

Dependent Variable: E1
Method: Least Squares
Date: 06/07/05   Time: 21:00
Sample(adjusted): 1991 2004
Included observations: 14 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
E2 0.501784 0.219561 2.285394 0.0413
C 0.006639 0.015069 0.440600 0.6673
R-squared 0.303258     Mean dependent var 0.007495
Adjusted R-squared 0.245197     S.D. dependent var 0.064877
S.E. of regression 0.056365     Akaike info criterion -2.782368
Sum squared resid 0.038124     Schwarz criterion -2.691074
Log likelihood 21.47658     F-statistic 5.223026
Durbin-Watson stat 1.517853     Prob(F-statistic) 0.041274

用1，2兩種修正，兩種效果都很好，都消除了自相關，相比較2更好。
所以，方程：b=0.502
Y*= Lｙ－o.502*Lｙ（－１） X*= Lx2－0.502*Lx2（－１）
Y*=1.2579+0.5862X*+et

以上就是通過分析和檢驗得到的回歸方程。所以，人均收入水平的高低在一定程度上影響房地產價格。當前的房地產價格增長背后收入是不可忽略的因素。

資料來源：中經網，國家統計局網站，

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